304
W. W. WILLMARTH AND S. S. LU
normality of u and u signals, for details see Willmarth and Lu (1971, 1972).
The predicted curves are included in Figs. 12-15 for comparison.
The assumption of joint normality of u and u signals also implies that the
contribution to i4P from the second quadrant cut should equal that from the
fourth quadrant
. Similarly, ; vl = cv,. Thc predicted curves for ;u2 and
; ul are also shown on the figures. The deviation from joint normality is
apparent since Cvz # cv, and # Gus, regardless of the flow speed and
the location in the turbulent boundary layer. As can be seen, the largest
contribution comes from the second quadrant which is burstlike. The second
largest contribution is Gu4 and is sweeplike. The contributions from i.hl and
; u3 are negative and relatively small. When the hole size H becomes large,
there are only two contributors. One is ;u2 and the other comes from the
hole region. Thus the importance of the burstlike events in the turbulent
boundary layer is obvious. At the hole size of H = 4.5. which amounts to
I ut, I > 10 1 uTJ, there is still a 15-30 0 4 contribution to It3 from the second
quadrant, i.e., uv,/ijii x 0.15 to 0.30. At this level there are almost no contributions from the other three quadrants.
3.6. Results jbr the Burstlike and Sweeplike Ewnts
Results will be discussed here regarding the contributions to i@ from
burst: and sweeplike events with H = 0. Both ;u2/U7i and &4/ilF are nearly
constant across the boundary layer except very close to the wall and near the
edge of the boundary layer. It is found that I&~/U'U' x -0.34 and &y4/
u'v' z -0.24, or zu2/iG x 0.77 and ;u4/iZ sz 0.55. Thus, burstlike events
account for 77 % of the local Reynolds stress, and the sweeplike events have
55 % to their account. This leaves 32 % of local Reynolds stress to the other
two negative contributors.
The ratio of the contribution to U7i from the burstlike events and from the
sweeplike events is plotted in Fig. 16 as a function of y/S. There is a sharp
rise near the wall, while for most of the boundary layer the ratio is nearly
constant with a value of 1.35. The single high speed measurement gave a
value of 1.25, which was measured at y/S = 0.014 or y+ = 265. The results
are replotted in Fig. 17 8s a function of y '. In thm figure, the results obtained
by Wallace PC al. (1972) at a much lower Rcynokls number in a channel flow
arc included. It turns out that contributions to in from the sweep period are
approximately the same as in Wallace et al. (1972) but that the present
results show larger contributions to iiii during the burst period. The reason
for this disagreement may be due to the difference in Reynolds number. The
results for the present measurements (Fig. 17) seem to scale with the wall
region variables even though the two flow conditions considered differ
greatly in Reynolds number (Re, = 4230 and 38.000). Although there is only
W. W. WILLMARTH AND S. S. LU
normality of u and u signals, for details see Willmarth and Lu (1971, 1972).
The predicted curves are included in Figs. 12-15 for comparison.
The assumption of joint normality of u and u signals also implies that the
contribution to i4P from the second quadrant cut should equal that from the
fourth quadrant
. Similarly, ; vl = cv,. Thc predicted curves for ;u2 and
; ul are also shown on the figures. The deviation from joint normality is
apparent since Cvz # cv, and # Gus, regardless of the flow speed and
the location in the turbulent boundary layer. As can be seen, the largest
contribution comes from the second quadrant which is burstlike. The second
largest contribution is Gu4 and is sweeplike. The contributions from i.hl and
; u3 are negative and relatively small. When the hole size H becomes large,
there are only two contributors. One is ;u2 and the other comes from the
hole region. Thus the importance of the burstlike events in the turbulent
boundary layer is obvious. At the hole size of H = 4.5. which amounts to
I ut, I > 10 1 uTJ, there is still a 15-30 0 4 contribution to It3 from the second
quadrant, i.e., uv,/ijii x 0.15 to 0.30. At this level there are almost no contributions from the other three quadrants.
3.6. Results jbr the Burstlike and Sweeplike Ewnts
Results will be discussed here regarding the contributions to i@ from
burst: and sweeplike events with H = 0. Both ;u2/U7i and &4/ilF are nearly
constant across the boundary layer except very close to the wall and near the
edge of the boundary layer. It is found that I&~/U'U' x -0.34 and &y4/
u'v' z -0.24, or zu2/iG x 0.77 and ;u4/iZ sz 0.55. Thus, burstlike events
account for 77 % of the local Reynolds stress, and the sweeplike events have
55 % to their account. This leaves 32 % of local Reynolds stress to the other
two negative contributors.
The ratio of the contribution to U7i from the burstlike events and from the
sweeplike events is plotted in Fig. 16 as a function of y/S. There is a sharp
rise near the wall, while for most of the boundary layer the ratio is nearly
constant with a value of 1.35. The single high speed measurement gave a
value of 1.25, which was measured at y/S = 0.014 or y+ = 265. The results
are replotted in Fig. 17 8s a function of y '. In thm figure, the results obtained
by Wallace PC al. (1972) at a much lower Rcynokls number in a channel flow
arc included. It turns out that contributions to in from the sweep period are
approximately the same as in Wallace et al. (1972) but that the present
results show larger contributions to iiii during the burst period. The reason
for this disagreement may be due to the difference in Reynolds number. The
results for the present measurements (Fig. 17) seem to scale with the wall
region variables even though the two flow conditions considered differ
greatly in Reynolds number (Re, = 4230 and 38.000). Although there is only